Question

How many solutions does
the equation
2x-3-m=m
​

Answer 1

We have to find the number of solutions of the equation ||2x - 3| - m| = m where m > 0.

solution : here m > 0 , it means ||2x - 3| - m| is positive term.

so, |2x - 3| - m = m

⇒|2x - 3| = 2m

⇒2x - 3 = ± 2m

⇒2x = 3 ± 2m

⇒x = (3 ± 2m)/2

also |2x - 3| = 0 ⇒2x = 3 ⇒x = 3/2

Therefore x = (3 + 2m)/2, (3 - 2m)/2 and 3/2 are the solutions of equation.

so there are three solutions of the given equation.